In both pre-plotted adventures and more story-telling ones, a lot of situations occur where monsters/npcs/magical items/geography appear, which wasn't thought of beforehand. I.e. I do not have the stats for them available.

How do you come up with these items/characters/details on the fly? Is it all just improvisation? They're obviously improvised, but what I am asking is; do these follow other gaming rules. For instance, a rule of "yes, but..", rather than the system combat rules. Since the cat following the party just revealed itself to be Tankors long-lost twin, a shape-shifting druid, I don't know what spells he can do or what AC, so all kind of rolls will be without values to check against. Is it ok to let the story decide rather than the dice?

...or.. Do you adapt items from books, monsters manuals, etc. Is it possible to pre-make lots of npcs and just pick a sort-of fitting for the new character and then fill in some details (initially left blank). In that case all the newly introduced game elements would fit into the system and the dice could rule again?

Maybe there are some other ways of solving this on-the-fly as the two I outlined. I can imagine that being very experienced with a system the GM would know what AC and skills a 5-th level ranger or a little blue dragon would probably have.. but I'm sort of looking for advice for those of us who can't pull stats off the top of our head.

7 Answers
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[...] monsters/npcs/magical items/geography appear, which wasn't thought of
beforehand. I.e. I do not have the stats for them available.

In a group with any decent imagination, this should be common place. Keep a book handy with Monster stats, and don't be afraid to take a short break while you figure out what you need.

How do you come up with these items/characters/details on the fly?
[..] do these follow other gaming rules.

You can handle this either way: make it up or use official rules. It helps to keep some common values (players AC, HP, saves, avg damage, etc) so you know that you're not throwing an impossible challenge at them.

Since the cat following the party just revealed itself to be [...] a shape-shifting druid

If this was planned, try to have the NPC outlined before the session starts. If it was a stroke of brilliance, take a short break and sketch him out. You don't need actual stats until battle starts either.

Is it possible to pre-make lots of npcs [...]

One trick I use is to keep old PC and NPC sheets. That gives me a wide range of characters to draw from, and occasionally provides some humorous nostalgia.

I can imagine that being very experienced with a system the GM would know what AC and
skills a 5-th level ranger or a little blue dragon would probably have.. but I'm sort of > looking for advice for those of us who can't pull stats off the top of our head.

Try keeping a notebook just for this campaign. Make notes of monster strengths as the party fights them (so you can easily re-use them) as well as anything the party has trouble with or breezes past. This will give you an idea of the challenges your party can handle, and what to avoid (or torment them with).

Is it ok to let the story decide rather than the dice?

Yes, but be careful. There's a fine line between GM intervention and dice rolls. It's important for the dice to make most the decisions, otherwise players feel cheated when they die (the GM killed me, not the bad roll!) or feel invulnerable (the GM always fudges so we live!).

tl;dr: Take breaks if you encounter an unexpected surprise, keep notes and old sheets for inspiration, and don't be afraid to fudge the rules a little (but not too much)!

It's always best to have as much material as possible ready to go, but as your question suggests, that's jut not always possible. For one thing, no matter how much prep you do, the players will do things that surprise you.

Wherever possible I use existing material and repurpose it with the current situation in mind. For that reason, I never get rid of old NPC writeups, encounter stats, and so on. The players don't need to know that the town guard they faced last week are now a band of brigands. Change a couple of weapons and bump the armor down a notch, and reduce their numbers from 6 to 5.

It's also useful to hone in on what is important about a character, place, or thing. A situation they encounter on the fly may turn out to be important in the overall progression of the game, and you may need to flesh out the details, but you usually don't have to fill in all the blanks on the spot. If it's an adversarial NPC, you don't need to know how they would react in any situation or what all of their capabilities are; you just need to know what they can and do in this moment. If it's a crypt, you don't need to know what ancient king is buried there, you just need to think of what kind of wards are in place, how many golems are guarding it, and what kind of treasure is there. You can figure out the rest later, when they go into town to hawk their loot.

Some gamemasters view this as sacrilege, but I like taking cues from player discussions. When they encounter something new and unexpected (to me as well as to them), they inevitably discuss what they think is really happening. If one of them has a good theory, sometimes I'll use it, perhaps tweaking it slightly. Yes, it does make sense that this would be the crypt of old Eathelwyld the Somnambulent.

Another potentially sacrilegious note: Game mechanics are there to advance the fun of the story. Without the story, the mechanics are meaningless. So when in doubt, fudge the numbers and advance the gameplay.

What I usually find works for me, is when the heroes are going to move through an area, I keep notes on what the culture is like. Is the area rural? Then I put down 2 or 3 example names to give me some inspiration in game just in case they ask "hey who is "

I adapt quite a bit from other books, sometimes bits of things from movies or things I see.

I take the approach a writer once said about writing:

"Everything is grist for the mill."

So I either take notes on my iphone or write down a description of something interesting I see on a napkin. Then use some part later in game. Such as: once I was on vacation and came across an unusual lantern in an antique shop. I took a quick photo with my iphone. Three months later the PCs suddenly became overly interested in a lantern that really had almost no special properties. But they really thought it did! So I whipped out the description of the old lantern and just let them oo and ah over it. Then I suggested that more research was needed (I kept saying they knew there was a part missing from it to make it work). That way to give me more time to prep before they tried to actually fiddle around with it!

So I suppose, I keep bits of things around in a notebook or in a doc file somewhere of items and ideas for use.

I do agree with @Erik Schmidt though... listen to the players. When they get to discussing the game, they will turn into a gold mine of inspiration. Use tidbits of what they think is happening, it will flush out your game, and enrich their ability to envision and immerse themselves in the game.

\$\begingroup\$I love the story of how you handled the lantern. It makes a good point about the value of giving them a little, but leaving the full details for later.\$\endgroup\$
– Erik SchmidtFeb 5 '12 at 1:23

\$\begingroup\$Thanks! It worked like a charm, too! I got a great side campaign out of that small thing too in the end.\$\endgroup\$
– Kummer WolfeFeb 5 '12 at 7:03

1

\$\begingroup\$+1 for "Then I suggested that more research was needed (I kept saying they knew there was a part missing from it to make it work). That way to give me more time to prep before they tried to actually fiddle around with it!" That's genius!\$\endgroup\$
– mghicksFeb 6 '12 at 14:31

\$\begingroup\$Along similar lines, I likewise invented a book entirely on the fly - something along the lines of a 'vampiric book' that if they put their name in it, it would record their 'adventures'. Then they realized it was cursed. They took it to a mage to get it removed (naturally) again... I whipped out the "I have to research this, it's a very rare item. I'll probably need some ingredients. I'll prepare you a list when I know more". Which buys me some time and a springboard for at least a couple of adventures!\$\endgroup\$
– Kummer WolfeFeb 6 '12 at 14:41

This sort of thing is really system dependent. A rules dense system like D&D/PF is going to be harder to wing it than a rules light FATE type system where the mentioned druid might have a couple aspects relating to personality & goals that might not even be important enough at this time to get noticed, you can fill in whatever stats/skills you need based on the situation... A few stress boxes is pretty much all you need to keep track of if combat starts up.

It helps to think of a couple details about the various factions/groups, how they interact/mesh together, what their individual interests are, and whoever represents them to the players (The king probably doesn't represent the royal court to a bunch of nobodies, that is probably more of a city guard with city guard interests that kowtow to the royal court for example). Once you have a basic framework in place, it's easier to wing it because you already have a good idea of who will be affected & how they will react to changing circumstances.

This is an addendum to the existing, perfectly good answers, but I wanted to point out a crucial fact: You ARE allowed to say no. Remember, you're playing the game too. If you're feeling overwhelmed and overworked, it's totally fine to go with a path of lesser resistance. The improv rule about not saying "no" is meant to stop you from shutting down the game, not to turn you into a procedural game generator who is constantly having to roll up new NPCs and invent new locales. As long as the game can continue and people are enjoying themselves, no one suggestion has to be taken at face value.

For example, that cat doesn't have to actually be a shape-shifting Druid after all. The PC could believe it's a Druid, which could be played for laughs and result in much merriment and enjoyment as he continues to try and "prove" it, which is a lot easier to play off for you than trying to come up with stats on the fly. If a player decides to ride to another country where you're not prepared with geography, feel free to stop them at the border with an over-zealous immigration officer, giving them an interesting encounter while giving you more time to consider what might be in that direction. If the players decide to go hunting for a specific magic item, maybe nobody has it in stock but someone heard a rumor it might be in [insert already-planned dungeon here] -- even if it's not, it'll mean the game keeps moving, and people can keep having fun.

General

I wrote myself a program that outputs random characters (and one for hunting results). Thats not easy, but for many systems such programs exist on the Internet. As I am also a GM that uses "real" names the namesettings for any region in the world cover the namesettings from a culture in real world (German, Russian, English, Somali...). As there are plentyful resources in the world to get to know names from a culture (ofter there are lists from statistical government units, or you use their politicians, astronauts, scientists, pop-culture...). Then I just randomize that List and just pick the next one whenever a name is needed.

As for items: There are loot lists for many a setting or you should write one yourself. Then just roll that list whenever loot is required. For everything else: deviantart.com! Just enter the name of object you need and images for it will pop up to you.
Important: Before showing said image to the players remove any dA mark from them (e.G. open image in own browser window, don't use image with dA watermark). So they don't know you just pulled it out of the net instead of having it prepared up front and handle everything the same.

For maps and stuff I use osm.org or google maps or some such and select an area that is likely to match the area where the group is. They don't need to know that they are actually playing in St. Pölten, Austria but reality is just so much more detailed than any preparation could be and you never have trouble creating that next batch of map: Just look it up and send it to your printer. Done.

Rules & Dice

With generated NPCs thats easy, but if you don't have them: use the monster from the book (if you have to look it up, look it up). For characters use the stats of a PC that comes close. There is no shame in looking at your players characters if you have to make up an NPC. And the players wont actually notice if you say: Frank, give me your character sheet for a moment. (If you mutter to yourself and roll some dice while scribbling the stats down they think something great is going to happen soon which increases tension even if nothing happens.)